My Odometer, Speedometer, and the Time I was driving from home to university earlier this week when I glanced at my dashboard just soon enough to notice the odometer tick up while simultaneously registering my speed and the time.  I thought to myself,
"How might I find the probability that the odometer will tick up once more before the minute space on the clock increments?"
That is my question.  If this belongs in physics, please move it.  Assume nonrelativistic velocity (unless, of course, you're into that sort of thing).
 A: I think I see what you are getting at.
Lets say you see your odometer tick up and you note the location of the minute hand and your speed. What is the probability that the odometer will tick again before the minute hand moves to the next minute.
We can model this as follows:
Let $T_1$ be the number of seconds into the given minute that your odometer first ticks up. Let V be the noted speed, in mph. And assume your odometer has increments of $\Delta d$ miles.
Lets assume that your odometer is equally likely to tick up for the first time near the beginning of the minute as towards the end, so that $T_1 \sim Uniform(0,60)$. Now, what is the number of seconds to get another tick given your noted velocity, V? It is: $T_2(V)=\frac{3600\Delta d}{V}$. The probability of getting two ticks in a minute, given your noted speed and the occurrance of a first tick, can be written as:
$P(T_1+T_2\leq 60|V)=P(T_1\leq 60-\frac{3600\Delta d}{V})=\frac{60-\frac{3600\Delta d}{V}}{60}=max\{0,1-\frac{60\Delta d}{V}\}$
